A moderate deviation principle for stochastic Volterra equation

2017 ◽  
Vol 122 ◽  
pp. 79-85 ◽  
Author(s):  
Yumeng Li ◽  
Ran Wang ◽  
Nian Yao ◽  
Shuguang Zhang
Keyword(s):  
Volterra Equation ◽  
Moderate Deviation ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Stochastic Volterra Equation

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

Moderate deviations for linear eigenvalue statistics of β-ensembles

2021 ◽  
pp. 2250017
Author(s):  
Fuqing Gao ◽  
Jianyong Mu
Keyword(s):  
Moderate Deviation ◽  
Main Ingredient ◽  
Moderate Deviation Principle ◽  
Uniform Estimates ◽  
Linear Eigenvalue Statistics ◽  
Deviation Principle ◽  
Eigenvalue Statistics ◽  
Real Analytic ◽  
The One ◽  
Analytic Potential

We establish a moderate deviation principle for linear eigenvalue statistics of [Formula: see text]-ensembles in the one-cut regime with a real-analytic potential. The main ingredient is to obtain uniform estimates for the correlators of a family of perturbations of [Formula: see text]-ensembles using the loop equations.

ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

2019 ◽  
Vol 34 (4) ◽  
pp. 570-582
Author(s):  
Yu Miao ◽  
Huanhuan Ma ◽  
Qinglong Yang
Keyword(s):  
Law Of Large Numbers ◽  
Moderate Deviation ◽  
Bernoulli Model ◽  
Strong Law ◽  
Asymptotic Behaviors ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Large Numbers ◽  
Bernoulli Variables ◽  
Image Position

AbstractWe consider a class of correlated Bernoulli variables, which have the following form: for some 0 < p < 1, $$\begin{align}{P(X_{j+1}=1 \vert {\cal F}_{j})= (1-\theta_j)p+\theta_jS_j/j,}\end{align}$$where 0 ≤ θj ≤ 1, $S_n=\sum _{j=1}^nX_j$ and ${\cal F}_n=\sigma \{X_1,\ldots , X_n\}$. The aim of this paper is to establish the strong law of large numbers which extend some known results, and prove the moderate deviation principle for the correlated Bernoulli model.

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